Transcendental Number Theory

Transcendental Number Theory is a branch of mathematics that studies numbers that are not roots of any non-zero polynomial equation with rational coefficients. In simpler terms, these are numbers that cannot be expressed as solutions to algebraic equations like integers or fractions can. Famous examples include numbers like \( e \) (the base of natural logarithms) and \( \pi \) (the ratio of a circle's circumference to its diameter), which are proven to be transcendental. This area of study explores their properties, relationships, and implications in both pure mathematics and various applications.